col19.z

#############################################################################
##
#W  col19.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 1845 ] :=
[ 21818575428879, 268700225759, 20316225759, 65759 ]; 

PROPERTIES_SMALL_GROUPS[ 1845 ] := rec(
isNilpotent := [ 2, 4 ], 
isAbelian := [ 2, 4 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 3, -4 ], [ 1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 1848 ] :=
[ 218415844003156485010059, 19870960893043209019005,
403632400786863952645010059, 3594575159305019005, 32250303349257015009,
17918559519241019005, 59756231155254021010059, 3586815689225059001,
59598581973123845050019, 33113511599014661090015, 110429515324600615811000159
, 448108953603000159, 218580437974422018001059, 218580437974422017001059,
403936649376743592451001059, 218580437974422048001059,
403936649376743592482001059, 403936649376743592481001059,
746474928048222170550819001059, 134584049864891466275001059,
39408477700610001059, 72826866809995810001059, 39408477700609001059,
39408477700640001059, 12262587561879339555001905, 3590692340226001905,
6635599330083362001905, 3590692340225001905, 3590692340256001905,
248711178561342336434979001059, 72826824179090178001059,
134583971082977444642001059, 72826824179090177001059, 72826824179090208001059
, 196972305715714001059, 196972305715713001059, 364004821034865155001059,
196972305715744001059, 364004821034865186001059, 364004821034865185001059,
672680909272503030307001059, 39408431534594005019, 39408431534593005019,
72826781502018051005019, 39408431534624005019, 72826781502018082005019,
72826781502018081005019, 134583892215755444771005019,
364248197162342914000159, 364248197162342913000159,
673130668356239628803000159, 364248197162342944000159,
673130668356239628834000159, 673130668356239628833000159,
1243945475122331063949859000159, 17918566867202009015, 17918566867201009015,
33113511577002243009015, 17918566867232009015, 33113511577002274009015,
33113511577002273009015, 61193769394306556195009015, 364004821196345986000159
, 364004821196345985000159, 672680909571080852099000159,
364004821196346016000159, 672680909571080852130000159,
672680909571080852129000159, 1243114320887357648147107000159,
509593755677887234000159, 509593755677887233000159,
941729260492972624643000159, 509593755677887264000159,
941729260492972624674000159, 941729260492972624673000159,
1740315673391013647354659000159, 673130668015192382210000159,
673130668015192382209000159, 1243945474492075751774979000159,
673130668015192382240000159, 1243945474492075751775010000159,
1243945474492075751775009000159, 2298811236861355989509610275000159,
5820710914001905, 5820710944001905, 19878122877943843001905,
12269187326043881880159000, 22673722932312914543052190050,
59598539284546083001509, 17451450882001509, 32250291814946001509,
17451450881001509, 17451450912001509, 33113484433556003001905,
9696182786001905, 17918552179234001905, 9696182785001905, 9696182816001905,
110429515025780572963001059, 32335622832898001059, 59756231074513698001059,
32335622832897001059, 32335622832928001059, 6628429582565923005901,
1940914690005901, 3586812543522005901, 1940914689005901, 1940914720005901,
110138179422419682083005019, 32250314883842005019, 59598581938520866005019,
32250314883841005019, 32250314883872005019, 61193769394306548515009015,
17918566859522009015, 33113511576994594009015, 17918566859521009015,
17918566859552009015, 204073744319414554067875000159, 59756231235994498000159
, 110429515324358394786000159, 59756231235994497000159,
59756231235994528000159, 242221057000159, 242221088000159,
827657963962403000159,
[ ( 1, 2)( 4, 5)( 8, 9,10,11,12,13,14,15,16,17,18), (2,3,4)(5,6,7) ],
113037042158263183983040195000, 39497543848448000159, 197104002697728000159,
25076667791360159000, 13246106486309248059100, 24478804848026943936051900,
24478804817005871552091500, 45236831359494980121056015900, 63955927552000159,
5818810880000195, 118190368752384000159, 118194195929600015009,
75214487558656019005, 1019950067381964544010059, 218935386700783104010059,
19928256821082624019005, 404592594623090663168010059, 106586706432000159,
21324894720000519, 197104002669056000159, 9696190720000915,
196972305715840000159, 275754196667136000159, 364248196977793792000159,
1310720000195, 5814366208015900, 3621696583680019005, 9437696000159,
5243392000195, 17497588480000159, 1049088000591, 17451451136000519,
9696183040000915, 32335622833024000159, 159 ]; 

PROPERTIES_SMALL_GROUPS[ 1848 ] := rec(
isNilpotent := [ 12, 124, -126, 162 ], 
isSupersolvable := [ 1, -86, 89, -126, 129, -130, 136, -138, 145, -152, 155,
-162 ], 
isSolvable := [ 1, -126, 128, -162 ], 
isAbelian := [ 12, 124, 162 ], 
lgLength := rec( lgLength := [ 4, 5, 6, false ], pos := [ [ 128, -131, 136,
-138, 145, -152, 155, -162 ], [ 13, -126, 132, -135, 139, -144, 153, -154 ],
[ 1, -12 ], [ 127 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95,
98, 101, 104 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 24, 29,
34, 41, 48, 55, 62, 69, 76, 83, 86, 87, 88, 93, 98, 103, 108, 113, 118, 123,
126 ] ) );

SMALL_GROUP_LIB[ 1850 ] :=
[ 8859902787937695, 55714505388479, 16850846021594287647, 31822008767,
30152470463, 2633643039, 55778166194111, 4785776943519, 103189935675492287,
4031 ]; 

PROPERTIES_SMALL_GROUPS[ 1850 ] := rec(
isNilpotent := [ 4, 10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7
] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1854 ] :=
[ 10487765894206997903, 4629456919438223, 191011672114839643,
10383427280977295, 410935742533734620803, 5708530736015, 4629349325681519,
4629458434843247, 8582787267891332207, 2507778838895, 5600936979311,
58884330211, 10383428796382319, 102921114606619, 19250884486697223407, 10607
]; 

PROPERTIES_SMALL_GROUPS[ 1854 ] := rec(
isNilpotent := [ 6, 16 ], 
isAbelian := [ 6, 16 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, 10, -11, 14, -16 ], [ 1,
-6, 8, -9, 12, -13 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 1860 ] :=
[ 38461832597063025929729, 9644597459275529729, 20682108134462729729,
20683613790456381059, 38468720976194846781059, 5530986365093129729,
5578429269854727119, 10287680561189765127119, 752965656329729,
2974463102729729, 21487542129929729, 2223565886753103, 40012796736081927119,
741721560407101, 39966859561963581059, 4135832695378683033,
74423802105525595501019, 185131032301019,
[ (1,2,3,4,5), ( 3, 4, 5)( 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,
     22,23,24,25,26,27,28,29,30,31,32,33,34,35,36) ],
9644596840281601019, 20683588398681602759, 742415155201019,
1446255803780091029, 2567472389451792891029, 238263808039799237127119,
443170680107372205547527119, 5578379193945601019, 752272012801019,
752967187202759, 1398862342713602759, 2973744576001019, 2999223417601019,
5531011125408001019, 6171033601019, 4132866815448353103,
238298242407265464327119, 7687131906717471483033, 443234730877597623797101019
, 68880296332801019, 22967806348802759, 128210639847897601019,
2223589190426133, 128117383978953601019, 213514590659616001019,
238471790113641657601019, 1692057601019, 2221974893717100,
5578379880567291029, 11548915201019, 1197504001773, 21512227795201019,
401241603571, 21487543660802759, 2223567417626133, 40012796736835201019, 1019
]; 

PROPERTIES_SMALL_GROUPS[ 1860 ] := rec(
isNilpotent := [ 18, 56 ], 
isSupersolvable := [ 1, -18, 20, -22, 25, -46, 49, -56 ], 
isSolvable := [ 1, -18, 20, -56 ], 
isAbelian := [ 18, 56 ], 
lgLength := rec( lgLength := [ 4, 5, false ], pos := [ [ 20, -24, 27, -34, 39
, -56 ], [ 1, -18, 25, -26, 35, -38 ], [ 19 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25,
27, 29, 31, 33, 35, 37 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18 ] ) );

SMALL_GROUP_LIB[ 1862 ] :=
[ 935831679058211, 1702354853087, 1757120091817226027, 1021418207, 917072063,
272099723, 1706441148863, 502277413091, 3177419781741119, 1727 ]; 

PROPERTIES_SMALL_GROUPS[ 1862 ] := rec(
isNilpotent := [ 4, 10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7
] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1870 ] :=
[ 3200595788703, 188552840185, 5985107499287455, 276825081, 505414559,
304088057, 946338792351, 102762995, 942916241727, 565831536441,
1769666485158815, 927 ]; 

PROPERTIES_SMALL_GROUPS[ 1870 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 1876 ] :=
[ 91195940027417, 1185306541145957, 2228522877471501467, 4556384381339,
6106162945107851, 632086406027, 49182520007, 1187910463120523, 395 ]; 

PROPERTIES_SMALL_GROUPS[ 1876 ] := rec(
isNilpotent := [ 4, 9 ], 
isAbelian := [ 4, 9 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -9 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 1880 ] :=
[ 35812224866706522171, 537005550102103039797, 1010692451657267237053783,
1492438965178088791, 67279243717816443076667, 5944746886240433109073995095,
1681968404102019985015, 1681968404101814022039, 3162100600256347820879191,
1681968404104903466679, 3162100600256350910323831, 3162100600256350704360855,
5944749128482478069586942807, 1009570136128495680992153, 285641108090062521,
537005391503402529977, 285641107884099545, 285641110973544185,
67326950994528259608215, 19049064591417783, 35812207996892762039,
19049064385454807, 19049067474899447, 1900101807625526999197897559,
537602367099112826487, 1010692450864263437784183, 537602367098906863511,
537602367101996308151, 793007094677399, 793010184122039,
2804295193433194638167, 3162123248533511105785463, 35786833460201235159,
3162099407574316323497879, 894663754668912823, 151878746206391,
10149855459353, 285958323615246519, 183 ]; 

PROPERTIES_SMALL_GROUPS[ 1880 ] := rec(
isNilpotent := [ 4, 29, -31, 39 ], 
isAbelian := [ 4, 29, 39 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, -39 ], [ 7, -34 ], [
1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 17, 20, 23, 26, 29, 32, 35 ],
pos := [ 1, 2, 3, 4, 5, 6, 13, 18, 23, 28, 31 ] ) );